The turbulence behaviour of current-dominated pulsating flows has been investigated. Direct numerical simulations have been carried out for Stokes lengths over a range of $l_s^+=5\unicode{x2013}26$, and amplitudes spanning 90 % of the current-dominated regime, about a mean flow of $\overline {Re}=6275$. The results show that the turbulence response in intermediate and low-frequency pulsations is governed by a multistage turbulent–turbulent transition process, which bears a strong similarity to the multistage response of non-periodic acceleration. During the early acceleration period, the flow enters a pretransition stage, in which a new laminar perturbation boundary layer forms at the wall, and the streamwise velocity streaks are stretched. If the low-speed streaks destabilise prior to the deceleration period, then the flow enters a transition stage in which the perturbation boundary layer undergoes a bypass-like transition process. A unique feature of pulsating flows is the ongoing mechanism of turbulence decay, which initiates during the deceleration period and constitutes the main transient turbulence mechanism for much of the cycle. For high-frequency pulsations, the perturbation boundary layer fails to reach the pretransition stage prior to the deceleration period. Instead, the flow alternates between two inertial stages which are characterised by two layers of amplified viscous force; one growing at the wall, and one detached and moving towards the core.

The current study investigates the global linear stability of a two-layer channel flow with a train of solid particles flowing near the liquid–liquid interface. Three different mechanisms of instability (shear, interfacial and migration modes) are identified, and their interactions are examined. The interfacial instability, associated with the viscosity jump at the liquid–liquid interface, is found to be coupled to the migration of the particle. The stability of the flow configuration is evaluated for various governing parameters, including fluid viscosities and flow rate ratios, particle position, inter-particle distance, and Reynolds and capillary numbers. Our numerical results are compared with the particle-free flow configuration, indicating that the presence of the particle in the more viscous fluid promotes the destabilization of the interface. Remarkably, under certain flow parameters, the presence of the particle stabilizes the interface when flowing in the less viscous liquid. The impact of particles is more significant as the capillary number increases or the Reynolds number decreases.

This study investigates the dynamics of fingering convection on scales much smaller than the typical size of individual salt fingers. On such scales, salinity patterns exhibit the spontaneous emergence of sharp fronts induced by finger-scale strain. In contrast, velocity and temperature fields are largely devoid of sub-microscale variability, which is attributed to the rapid molecular dissipation of heat and momentum. The presence of fine salinity structures fundamentally limits the efficiency of direct numerical simulations (DNS) of double-diffusive processes. In the oceanographic context, the computational cost of resolving sub-microscale salinity features exceeds that of temperature-only DNS by up to four orders of magnitude, severely restricting the types of double-diffusive systems that can be studied numerically. To address this complication, we introduce the sub-microscale filtering (SMF) algorithm, which resolves temperature and velocity while parameterizing the sub-microscale dynamics of salinity. The proposed closure draws inspiration from the Smagorinsky scheme, which represents unresolved processes by the downgradient strain-dependent momentum flux. The SMF model is successfully validated through fully resolved simulations.

Recent measurements of inertial particles in isotropic turbulence (Hammond & Meng, J. Fluid Mech., vol. 921, 2021, A16) revealed surprising extreme clustering of particles at near-contact separations $(r)$, whereby the radial distribution function, $g(r)$, grows from $O(10)$ to $O(10^3)$ with a $(r/a)^{-6}$ scaling (where $a$ is the particle radius), and a surprising upturn of the mean inward particle-pair relative velocity (MIRV). Hydrodynamic interactions (HIs) were proposed to explain the extreme clustering, but despite predicting the correct scaling $(r/a)^{-6}$, the HI theory underpredicted $g(r)$ by at least two orders of magnitude (Bragg et al., J. Fluid Mech., vol. 933, 2022, A31). To further understand the extreme clustering phenomenon and the relevance of HI, we characterize $g(r)$ and particle-pair kinematics for Stokes numbers $0.07 \leq St \leq 3.68$ in a homogeneous isotropic turbulence chamber using three-dimensional (3-D) particle tracking resolved to near–contact. A drift–diffusion equation governing $g(r)$ is presented to investigate the kinematic mechanisms of particle pairs. Measurements in all 24 conditions show that when $r/a\lessapprox 20$, extreme clustering consistently occurs, scaling as $g(r) \sim (r/a)^{-k}$ with $4.5 \leq k \leq 7.6$, which increases with $St$. Here $g(r)$ varies with $St$, particle size, density and polydispersity in ways that HI cannot explain. The extreme clustering region features an inward drift contributed by particle-pair turbophoresis and an inward radial relative acceleration. The latter indicates an interparticle attractive force at these separations that HI also cannot explain. The MIRV turns upward when approaching the extreme clustering region, opposite to direct numerical simulation predictions. These observations further support our previous assessment that extreme clustering arises from particle–particle interactions, but HI is not the main mechanism.

The impact of bulk viscosity is unclear with considering the increased dilatational dissipation and compressibility effects in hypersonic turbulence flows. In this study, we employ direct numerical simulations to conduct comprehensive analysis of the effect of bulk viscosity on hypersonic turbulent boundary layer flow over a flat plate. The results demonstrate that the scaling relations remain valid even when accounting for large bulk viscosity. However, the wall-normal velocity fluctuations $v_{rms}^{\prime \prime }$ decrease significantly in the viscous sublayer due to the enhanced bulk dilatational dissipation. The intensity of travelling-wave-like alternating positive and negative structures of instantaneous pressure fluctuations $p_{rms}^{\prime }$ in the near-wall region decreases distinctly after considering the bulk viscosity, which is attributed mainly to the reduction of compressible pressure fluctuations $p_{c,rms}^{+}$. Furthermore, the velocity divergence $\partial u_{i} / \partial x_{i}$ undergoes a significant decrease by bulk viscosity. In short, our results indicate that bulk viscosity can weaken the compressibility of the hypersonic turbulent boundary layer and becomes more significant as the Mach number increases and the wall temperature decreases. Notably, when the bulk-to-shear viscosity ratio of the gas reaches a few hundred levels ($\mu _b/\mu =O(10^2)$), and mechanical behaviour of the near-wall region ($\kern 0.06em y^+\le 30$) is of greater interest, the impact of bulk viscosity on the hypersonic cold-wall turbulent boundary layer may not be negligible.

We perform a linear stability analysis of a finite-amplitude plane inertial wave (of frequency $\omega$ in the range $0\le \omega \le f$, where $f$ is the Coriolis frequency) by considering the inviscid evolution of three-dimensional (3-D), small-amplitude, short-wavelength perturbations. Characterizing the base flow plane inertial wave by its non-dimensional amplitude $A$ and the angle $\varPhi$ that its wavevector makes with the horizontal axis, the local stability equations are solved over the entire range of perturbation wavevector orientations. At sufficiently small $A$, 3-D parametric subharmonic instability (PSI) is the only instability mechanism, with the most unstable perturbation wavevector making an angle close to $60^{\circ }$ with the inertial wave plane. In addition, the most unstable perturbation is shear-aligned with the inertial wave in the inertial wave plane. Further, at large $\varPhi$, i.e. $\omega \approx f,$ there exists a wide range of perturbation wavevectors whose growth rate is comparable to the maximum growth rate. As $A$ is increased, theoretical PSI estimates become less relevant in describing the instability characteristics, and the dominant instability transitions to a two-dimensional (2-D) shear-aligned instability, which is shown to be driven by third-order resonance. The transition from 3-D PSI to a 2-D shear-aligned instability is shown to be reasonably captured by two different criteria, one based on the nonlinear time scale in the inertial wave and the other being a Rossby-number-based one.

We examine the vapour cloud of a pure liquid evaporating from a millimetric cylindrical well/cavity/aperture. This is accomplished by injecting the liquid up a vertical pipe towards its outlet onto a horizontal substrate. The injection is halted before the liquid surpasses the substrate level. The resulting final state is a meniscus at or near the pipe's end. The analysis is realised by vapour interferometry (side view over the substrate) closely intertwined with simulations (including Stefan flow), which also help to fill up certain gaps in the measurements and provide computed evaporation rates. Comparison with experiment is facilitated by converting the computed vapour clouds into interferometric images, especially helpful when an inverse (Abel-type) conversion is difficult. Experiments are conducted in both microgravity (via parabolic flights) and ground conditions, thus enabling direct assessment of the role of gravity. The contrast is accentuated by a working liquid with heavy vapour (refrigerant HFE-7100), when instead of being flattened on ground the vapour cloud assumes a roughly hemispherical shape in microgravity. Furthermore, a non-trivial vapour-cloud response to the flight ${\rm g}$-jitter (residual gravity oscillations) is unveiled, ${\rm g}$-jitter vibrations posing a challenge for interferometry itself. A number of undesired but curious side issues are revealed. One concerns vapour formed deep inside the pipe during rapid injection and subsequently ejected into the field of view, which is detected experimentally and quantified in terms of vapour Taylor dispersion in the pipe. Others are an injection volume anomaly and parasitic postinjection specifically observed in microgravity conditions.

The objective of this three-part work is to formulate and rigorously analyse a number of reduced mathematical models that are nevertheless capable of describing the hydrology at the scale of a river basin (i.e. catchment). Coupled surface and subsurface flows are considered. In this first part, we identify and analyse the key physical parameters that appear in the governing formulations used within hydrodynamic rainfall–runoff models. Such parameters include those related to catchment dimensions, topography, soil and rock properties, rainfall intensities, Manning's coefficients and river channel dimensions. Despite the abundance of research that has produced data sets describing properties of specific river basins, there have been few studies that have investigated the ensemble of typical scaling of key physical properties; these estimates are needed to perform a proper dimensional analysis of rainfall–runoff models. Therefore, in this work, we perform an extensive analysis of the parameters; our results form a benchmark and provide guidance to practitioners on the typical parameter sizes and interdependencies. Crucially, the analysis is presented in a fashion that can be reproduced and extended by other researchers and, wherever possible, uses publicly available data sets for catchments in the UK.

We describe theoretically ‘electrolubrication’ in liquid mixtures: the phenomenon whereby an electric field applied transverse to the confining surfaces leads to concentration gradients that alter the flow profile significantly. When the more polar liquid is the less viscous one, the stress in the liquid falls on two electric-field-induced thin lubrication layers. The thickness of the lubrication layer depends on the Debye length and the mixture correlation length. For the simple case of two parallel and infinite plates, we calculate explicitly the liquid velocity profile and integrated flux. The maximum liquid velocity and flux can be increased by a factor $\alpha$, of order 10–100 or even more. For a binary mixture of water and a cosolvent, with viscosities $\eta _w$ and $\eta _{cs}$, respectively, $\alpha$ increases monotonically with inter-plate potential $V$ and average ion content, and is large if the ratio $\eta _{cs}/\eta _w$ is large.

The objective of this three-part work is to formulate and rigorously analyse a number of reduced mathematical models that are nevertheless capable of describing the hydrology at the scale of a river basin (i.e. catchment). Coupled surface and subsurface flows are considered. In this second part, we construct a benchmark catchment scenario and investigate the effects of parameters within their typical ranges. Previous research on coupled surface–subsurface models have focused on numerical simulations of site-specific catchments. Here, our focus is broad, emphasising the study of general solutions to the mathematical models, and their dependencies on dimensionless parameters. This study provides a foundation based on the examination of a geometrically simple three-dimensional benchmark scenario. We develop a non-dimensional coupled surface–subsurface model and extract the key dimensionless parameters. Asymptotic methods demonstrate under what conditions the model can be reduced to a two-dimensional form, where the principal groundwater and overland flows occur in the hillslope direction. Numerical solutions provide guidance on the validity of such reductions, and demonstrate the parametric dependencies corresponding to a strong rainfall event.

The objective of this three-part work is to formulate and rigorously analyse a number of reduced mathematical models that are nevertheless capable of describing the hydrology at the scale of a river basin (i.e. catchment). Coupled surface and subsurface flows are considered. In this third part, we focus on the development of analytical solutions and scaling laws for a benchmark catchment model that models the river flow (runoff) generated during a single rainfall. We demonstrate that for catchments characterised by a shallow impenetrable bedrock, the shallow-water approximation allows a reduction of the governing formulation to a coupled system of one-dimensional time-dependent equations for the surface and subsurface flows. Asymptotic analysis is used to derive semi-analytical solutions for the model. We provide simple asymptotic scaling laws describing the peak flow formation, and demonstrate its accuracy through a comparison with the two-dimensional model developed in Part 2. These scaling laws can be used as an analytical benchmark for assessing the validity of other physical, conceptual or statistical models of catchments.

We study theoretically and experimentally pressure-driven flow between a flat wall and a parallel corrugated wall, a design used widely in microfluidics for low-Reynolds-number mixing and particle separation. In contrast to previous work, which focuses on recirculating helicoidal flows along the microfluidic channel that result from its confining lateral walls, we study the three-dimensional pressure and flow fields and trajectories of tracer particles at the scale of each corrugation. Employing a perturbation approach for small surface roughness, we find that anisotropic pressure gradients generated by the surface corrugations, which are tilted with respect to the applied pressure gradient, drive transverse flows. We measure experimentally the flow fields using particle image velocimetry and quantify the effect of the ratio of the surface wavelength to the channel height on the transverse flows. Further, we track tracer particles moving near the surface structures and observe three-dimensional skewed helical trajectories. Projecting the helical motion to two dimensions reveals oscillatory near-surface motion with an overall drift along the surface corrugations, reminiscent of earlier experimental observations and independent of the secondary helical flows that are induced by confining lateral walls. Finally, we quantify the hydrodynamically induced drift transverse to the mean flow direction as a function of distance to the surface and the wavelength of the surface corrugations.